This episode is special because it is our first episode topic that was suggested by a listener. A huge shoutout to our friend Erick Lee (Twitter handle @TheErickLee) who suggested this great report published by OECD. If you are on Twitter, please give Erick a follow!

Every three years the OECD administers and publishes the Programme for International Student Assessment, better known as PISA, which evaluates 15 year-old students around the world to determine how well their education system has prepared them for life after compulsory schooling. This test is important because it allows the performance of educational systems to be examined and compared on a common measure across countries. Currently 70 countries participated in the latest PISA.

Ten Questions for Mathematics Teachers… and How PISA Can Help Answer Them is a report that takes the findings from analyses of the 2012 PISA and organizes them into ten questions that discuss what we know about mathematics teaching and learning around the world – and how these data might help you in your mathematics classes right now.

The questions encompass four broad categories:

teaching strategies

student learning strategies

curriculum coverage

various student characteristics, and how they are related to student achievement in mathematics and to each other.

Each question concludes with concrete, evidence-based suggestions to help teachers develop their mathematics teaching practice.

For the next several weeks, Maggie and I will tackle one new question from this report. Of course, we begin with Question #1: How much should I direct student learning in my mathematics classes?

WHERE DOES MATHEMATICS TEACHING FALL IN THE TEACHER- VS. STUDENT DIRECTED LEARNING DEBATE?

For years, the most common teaching strategy has been teacher directed with a small – but vocal – contingent calling for a more student-oriente

d teaching. Which one is better? Unfortunately, it is not a simple “either/or” proposition. It would have been so nice if the data simply said “do THIS and not THAT”. Rather, it is a bit more nuanced.

It depends on the the content and students being taught.

It is a given that most teachers are directly teaching. Student-centered practices are most commonly used within the context of differentiating instruction. The PISA survey indicates that students may be exposed to different teaching strategies based on their socio-economic status or gender. Girls reported being less frequently exposed to student-oriented instruction in mathematics class than boys did. Disadvantaged students, who are from the bottom quarter of the socio-economic distribution in their countries, reported more frequent exposure to these student-oriented strategies than advantaged students did.

The data show that as the instruction becomes more teacher-directed the more student learning relies upon using memorization skills. Conversely, the more student-oriented the instruction, the less students rely upon memorization and are increasingly able to elaborate upon their thinking.

WHICH TEACHERS USE ACTIVE-LEARNING TEACHING PRACTICES IN MATHEMATICS?

From the Teaching and Learning International Study (TALIS) – a different OECD-led survey – four active-learning (student-oriented) teaching practices are identified:

placing students in small groups

encouraging students to evaluate their own progress

assigning students long projects

using ICT (Information and Communications Technology) for class work.

These practices have been shown by many research studies to have positive effects on student learning and motivation. TALIS data show that teachers who are confident in their own abilities are more likely to engage in active-teaching practices – which is the bottom line, really. If a teacher feels comfortable with the necessary pedagogy, content knowledge, and classroom management, then they will be able to flexibly think about how to teach it in a manner other than direct instruction.

If this doesn’t scream “WE NEED MATH COACHES!!!”, then nothing does.

HOW CAN A VARIETY OF TEACHING STRATEGIES BENEFIT STUDENT ACHIEVEMENT?

As stated above, as the instruction becomes more teacher-directed the student learning becomes more reliant upon memorization. Conversely, the more student-oriented the instruction, the more students are able to elaborate upon their thinking.

The data indicate that students are slightly more successful in solving the easiest mathematics problems in PISA when teachers direct student learning. Yet as the problems become more difficult, students with more exposure to direct instruction no longer have a better chance of success. Students exposed to greater amounts of student-oriented teaching are more likely to solve the difficult problems on PISA.

This means that one teaching method is not sufficient to teach all math problems; teaching complex math skills might require different instructions strategies than those used to teach basic math skills. In fact, rather than succumbing to an “either/or” mentality (or a direct-instruction versus constructivist debate), Singapore is using this research to require teachers to use a variety of teaching methods depending on the complexity of the mathematics being learned.

Teacher-directed and student-oriented instruction must work in tandem.

WHAT CAN TEACHERS DO?

So, let’s wrap this up. What are teachers supposed to take from Question 1? Three things…

Plan math lessons that strive to reach all levels of learners (differentiation)

Make sure each lesson/unit has extension activities for those who can go deeper. (This is the low-floor/high-ceiling concept that Jo Boaler talks about.) Offer support for the struggling learner. And provide a variety of activities and roles for students with different abilities/interests

Provide a mix of teacher-directed and student-oriented teaching strategies

This requires that the teacher move beyond the textbook provided lessons and homework and add new activities to lessons that allow students to work together or use new tools (technology or games).

Let the difficulty of the mathematics problem guide the teaching strategy.

Reserve your teacher-directed lessons for simpler math concepts and research other strategies for teaching more difficult concepts.